Conjugate variables of thermodynamics 


Pressure  Volume 
Temperature  Entropy 
Chem. potential  Particle no. 
The amount of space occupied by an object or system is called the volume of the object or system. The volume of an object is one of the physical properties of the object. (For other meanings of the term, see Additional meanings of "volume" below.)
The volume of a solid object is given a numerical value that quantifies the amount of threedimensional space it occupies. A onedimensional object, such as a line in mathematics, or a twodimensional object, such as a square, is assigned zero volume in threedimensional space. In the thermodynamics of nonviscous fluids, volume is regarded as a "conjugate variable" to pressure. If pressure on the fluid is increased, its volume decreases; conversely, if pressure on the fluid is decreased, its volume increases.
Contents 
Volume is sometimes distinguished from the capacity of a container. The term capacity is used to indicate how much a container can hold (commonly measured in liters or its derived units), and volume indicates how much space the object displaces (commonly measured in cubic meters or its derived units). Alternatively, in a capacity management setting, capacity is defined as volume over a specified time period.
Common equations for volume:  

Shape  Equation  Variables 
A cube:  s = length of a side  
A rectangular prism:  l = length, w = width, h = height  
A cylinder (circular prism):  r = radius of circular face, h = distance between faces  
Any prism that has a constant cross sectional area along the height:  A = area of the base, h = height  
A sphere:  r = radius of sphere which is the first integral of the formula for Surface Area of a sphere 

An ellipsoid:  a, b, c = semiaxes of ellipsoid  
A pyramid:  A = area of base, h = height from base to apex  
A cone (circularbased pyramid):  r = radius of circle at base, h = distance from base to tip  
Any figure (integral calculus required)  h = any dimension of the figure, A(h) = area of the crosssections perpendicular to h described as a function of the position along h. (This will work for any figure, no matter if the prism is slanted or the crosssections change shape). 
Mathematically, the volume of a body may be defined by means of integral calculus. In this approach, the volume of the body is taken to be approximately equal to the sum of volumes of a large number of small cubes or concentric cylindrical shells, and adding the individual volumes of those shapes.
U.S. customary units of volume include the following:
The acre foot is often used in measuring the volume of water in a reservoir or aquifer. It is the volume of water that would cover an area of one acre to a depth of one foot. It is equivalent to 43,560 cubic feet or 1233.481 cubic meters.
The United Kingdom is increasingly using units of volume according to the SI metric system, namely, the cubic meter and liter. However, some former units of volume are still being used in varying degrees.
Imperial units of volume:
Traditional cooking measures for volume also include:
The volume of an object is equal to its mass divided by its average density (the term "average density" is used for an object that does not have uniform density). This is a rearrangement of the calculation of density as mass per unit volume.
The term "specific volume" is used for volume divided by mass, expressed in units such as cubic meters per kilogram (m³•kg^{1}). It is the reciprocal of density.
List of orders of magnitude for volume  

Factor (meters³*)  Multiple  Value 
10^{−105}  —  4×10^{−105} m^{3} is the Planck volume 
10^{−45}  —  Volume of a proton 
10^{−33}  —  Volume of a hydrogen atom (6.54×10^{32} meters^{3}) 
10^{−21}  1 attoliter  Volume of a typical virus (5 attoliters) 
10^{−15}  1 picoliter  A small grain of sand (0.063 millimeter diameter, 3 micrograms, 130 picoliters) 
10^{−12}  1 nanoliter  A medium grain of sand (0.5 millimeter diameter, 1.5 milligrams, 62 nanoliters) 
10^{−9}  1 microliter  A large grain of sand (2.0 millimeter diameter, 95 milligrams, 4 microliters) 
10^{−6}  1 milliliter (1 cubic centimeter) 
1 teaspoon = 3.55 mL to 5 mL 1 tablespoon = 14.2 mL to 20 mL 
10^{−3}  1 liter (1 cubic decimeter) 
1 U.S. quart = 0.95 liters; 1 United Kingdom quart = 1.14 liters 
10^{0}  1000 liters  Fuel tank for a 12passenger turboprop airplane 
10^{3}  1000 cubic meters (1 million liters) 
A mediumsize forest pond. An Olympicsize swimming pool, 25 meters by 50 meters by 2 meters deep, holds at least 2.5 megaliters. 
10^{6}  1 million cubic meters  — 
10^{9}  1 cubic kilometer (km^{3})  Volume of Lake Mead (Hoover Dam) = 35.2 km^{3} Volume of crude oil on Earth = ~300 km^{3} 
10^{12}  1000 cubic kilometers  Volume of Lake Superior = 12,232 km^{3} 
10^{15}  —  — 
10^{18}  —  Volume of water in all Earth oceans = 1.3×10^{18} 
10^{21}  —  Volume of Earth = ~1×10^{21} m^{3} 
10^{24}  —  Volume of Jupiter = ~1×10^{25} m^{3} 
10^{27}  —  Volume of the Sun = ~1×10^{27} m^{3} 
10^{30}  —  Volume of a red giant the same mass as the Sun = ~5×10^{32} m^{3} 
10^{33}  —  Volume of Betelgeuse = ~2.75×10^{35} m^{3} 
10^{54}  —  Volume of small dwarf galaxy like NGC 1705 = ~3×10^{55} m^{3} 
10^{57}  —  Volume of dwarf galaxy like the Large Magellanic Cloud = ~3×10^{58} m^{3} 
10^{60}  —  Volume of galaxy like the Milky Way = ~3.3×10^{61} m^{3} 
10^{66}  —  Volume of the Local Group (galaxy group that includes the Milky Way) = ~5×10^{68} m^{3} 
10^{72}  —  Volume of the Virgo Supercluster = ~4×10^{73} m^{3} 
10^{81}  —  Approximate volume of the observable universe 1.6×10^{81} m^{3} 
Besides the above meaning, the term "volume" can refer to the following concepts:
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